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Tabl e 1.
Basic symbols for system modelling by RBD [14]
No Graphical
symbol
Symbol Name
Description
1
B
Reliability block symbol corresponding to the particular system
2
N
Node m/n
node opens and closes the threshold structure
m from n or in which a parallel group of all
elements consists of m from all n elements that
must have fitness for individual subsystem use
Each reliability structure can be represented by sets of characteristic elements
of the system, known as cut-sets (analysis oriented on system failure) or path-sets
(analysis focused on the fitness for system use).
In Fig. 1 graphic representation of paths and cut-sets of the system is pre-
sented.In this case, the 5-element system with a complex reliability structure
consists of elements designated as
E
5
(Fig. 1). The system
was subjected to a searching process for the purpose of finding the minimal
path-sets and the minimal cut-sets.
E
1
,E
2
,E
3
,E
4
and
Fig. 1.
Graphic representation of path-sets and cut-sets of the system A) exemplary
system; B) minimal path-sets; C) minimal cut-sets
In Fig. 1B elements connected by lines form the minimal path-sets of the
considered system. The set of all minimal path-sets is as follow:
P
=
{{E
1
,E
3
,E
5
},
(
E
2
,E
3
,E
5
}, {E
4
,E
5
}}
(3)
Analogically, in Fig. 1C the minimal cut-sets of the system are presented. The
cut-sets are formed by the elements connected by lines. The set of all minimal
cut-sets can be represented in the following form:
ʩ
=
{{E
1
,E
2
,E
4
}, {E
3
,E
4
}, {E
5
}}
(4)
Reliability structure model can be converted to an equivalent model. An ex-
ample of the different ways to represent the reliability structure of the system is
shown in Fig. 2.
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